Chapter 4.5, Problem 24E

Solution

To find: The transformation required to obtain the graph of the function $y=2\tan x$ from a basic trigonometric function.

The function $y=2\tan x$ is obtained from $y=\tan x$ by the vertical stretch of graph $y=\tan x$ by a factor of $2$ .

Given information:

The function $y=2\tan x$ .

Explanation:

Consider the function $y=2\tan x$ ,

Its parent function is $y=\tan x$ .

Compare it with the function of the form as given below.

  $y=a\tan \left(b\left(x-h\right)\right)+k$  ...... (1)

The function $y=2\tan x$ can be written as the following.

  $y=2\tan \left(x-0\right)+0$  ...... (2)

Compare equation (1) and (2),

  $a=2$

The effect of $2$ is the vertical stretch of graph $y=\tan x$ by a factor of $2$ .

Graph the functions $y=\tan x$ and $y=2\tan x$ on the same window.

  

Thus, the function $y=2\tan x$ is obtained from $y=\tan x$ by the vertical stretch of graph $y=\tan x$ by a factor of $2$ .